cp's OEIS Frontend

A295101 Number of squarefree sqrt(n)-smooth numbers <= n.

%I A295101 #12 Mar 25 2020 06:54:46
%S A295101 1,1,1,2,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,7,7,7,7,7,8,8,8,8,8,
%T A295101 8,8,8,8,8,8,8,8,8,8,8,8,8,8,13,13,13,13,13,13,13,13,13,13,13,13,13,
%U A295101 13,13,13,13,13,13,13,13,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14
%N A295101 Number of squarefree sqrt(n)-smooth numbers <= n.
%C A295101 a(n) = number of positive squarefree integers m<=n such that A006530(m) <= sqrt(n).
%H A295101 Robert Israel, <a href="/A295101/b295101.txt">Table of n, a(n) for n = 1..10000</a>
%F A295101 a(n) = A013928(n+1) - Sum_{prime p > sqrt(n)} A013928(floor(n/p)+1).
%F A295101 If n is in A295102, then a(n)=a(n-1)+1; if n is in A001248, i.e., n=p^2 for prime p, then a(n)=a(n-1)+A013928(p); otherwise a(n)=a(n-1).
%p A295101 N:= 200: # for a(1)..a(N)
%p A295101 V:= Vector(N,1):
%p A295101 for n from 2 to N do
%p A295101    if not numtheory:-issqrfree(n) then next fi;
%p A295101    m:= max(max(numtheory:-factorset(n))^2,n);
%p A295101    if m <= N then V[m..N]:= map(`+`,V[m..N],1) fi;
%p A295101 od:
%p A295101 convert(V,list); # _Robert Israel_, Mar 24 2020
%Y A295101 Cf. A005117, A013928, A295084.
%K A295101 nonn,look
%O A295101 1,4
%A A295101 _Max Alekseyev_, Nov 14 2017